Development of ARMA Models for A Transient Calculation using Linearized Least-Squares Method

Abstract

The present paper deals with a modeling method of electric equipments for a transient calculation. The model developed in the paper is expressed as an ARMA model which is suited for a discrete time domain simulation. Parameters of the ARMA model have been conventiaonally evaluated by a non-linear optimization method. The non-linear optimization method inherently involves numerical instabilities. For example, there is no assurance of convergence into an optimum value which minimizes the sum of square errors. In this paper, a linearized least-squares method (LLS) is proposed for improving the numerical stability. The LLS always gives the optimized parameters of the ARMA model without an iterative calculation, and a very small calculation time is required. The proposed modeling method is applied to an LCR series circuit, a transformer, and a frequency-dependent overhead line. Transient responses evaluated by the proposed model agree well with the measured results and the exact solution.